Effect of Pauli blocking on coherent states of composite bosons

TL;DR

This paper investigates how Pauli blocking affects the quantum coherence of composite bosons made of fermions, revealing density-dependent limitations and differences from elementary boson behavior.

Contribution

It demonstrates the conditions under which the quantum nature of cobosons can be erased and how Pauli exclusion influences their coherent states at various densities.

Findings

Complete erasure possible for Frenkel-like cobosons at moderate densities

Pauli exclusion causes eigenvalues to decrease and correlation functions to increase at high densities

Coherent states of Wannier-like cobosons are more complex and differ from elementary bosons

Abstract

The quantum nature of elementary bosons can be completely erased by using coherent states known as Glauber states. Here, we consider composite bosons (cobosons) made of two fermions and look for the possibility to erase the bosonic quantum nature of the field and the fermionic quantum nature of its constituents, when the distribution of the coboson Schmidt decomposition is either flat like Frenkel excitons, or localized like Wannier excitons. We show that for Frenkel-like cobosons, complete erasure of the field quantum nature is possible up to a density which corresponds to a sizable fraction of the number of fermion-pair states making the coboson at hand. At higher density, the Pauli exclusion principle between fermionic constituents shows up dramatically. It induces: (i) the decrease of number-operator eigenvalues down to 1 and the increase of the number-state second-order correlation function up to 2; (ii) the disappearance of the usual sharp peak in the coherent-state distribution and the increase of the coherent-state second-order correlation function up to 2. It also is possible to construct number states and coherent states for Wannier-like cobosons, but their forms are far more complex. Finally, we show that Pauli blocking makes the coboson coherent states qualitatively different from the Anderson's ansatz.